PD Peter Massopust, Ph.D.

Privatdozent
Technische Universität München
Zentrum Mathematik - M15
Boltzmannstraße 3
85748 Garching

Room: 02.10.038
Phone: +49-89-289-17488
eMail: massopust"at"ma.tum.de

News

I was awarded a GIAN lectureship under the GIAN initiative (Global Initiative of Academic Networks ). The lecturship is comprised of a two-week long lecture series on "Splines and Fractals in Approximation and Interpolation Theory" and will be held at IIT Madras, India, from July 15 - 31, 2016.

Research Interests

• Efficient Representations of Multidimensional Data via Frames, Wavelets, and Fractals
• Abstract and Applied Harmonic Analysis
• Functional Analysis
• Wavelets, Splines, and Frames
• Approximation and Interpolation Theory
• Fractal Analysis and Fractal Geometry

Recently Organized Conferences and Workshops

• Symposium on Higher-dimensional Splines: Variations on a Theme , ICNAAM 2014, September 22 - 28, 2014, Rhodes, Greece (with Patrick Van Fleet, University of St. Thomas, St. Paul, Minnesota, USA)
• SampTA 2013 , July 1 - 5, 2013 at the Jacobs University, Bremen, Germany (with Götz Pfander, Werner Henkel, Peter Oswald, Jacobs University Bremen, Peter Maaß, University of Bremen, Holger Rauhut, RWTH Aachen)
• Summer School on New Trends and Directions in Harmonic Analysis, Fractional Operator Theory and Image Analysis, Sept. 17 - 22, 2012 in Inzell, Germany (with Brigitte Forster, Universität Passau)

Recent Publications (last ten years)

Monographs

• P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 2nd ed., 426 pp., August 2016.

Text books

• P. Massopust, Interpolation and Approximation with Splines and Fractals , Oxford University Press, 336 pp., Jan. 2010.
• B. Forster and P. Massopust, Eds., Contributors: O. Christensen, K. Gröchenig, D. Labate, P. Vandergheynst, G. Weiss, Y. Wiaux, Four Short Courses in Harmonic Analysis , Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag , approx. 250 pp., Nov. 2009.

Edited books

• D. Larson, P. Massopust, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed, eds., Frames and Operator Theory in Analysis and Signal Processing, Contemporary Mathematics, AMS Book Series, Vol. 451, 291 pp., 2008.
• E. Grinberg, D. Larson, P. Massopust, P.E.T. Jorgensen, G. Olafsson, E.T. Quinto, and B. Rubin, eds., Radon Transforms, Geometry, and Wavelets, Contemporary Mathematics, AMS Book Series, 2008.

Special Issues Edited

• Numerical Functional Analysis and Optimization: Special Issue on Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, Vol. 33, Issue 7--9, 2012 (with P. G. Casazza, Palle E. T. Jorgensen, Keri A. Kornelson, Gitta Kutyniok, David R. Larson, Gestur \'{O}lafsson, Judith A. Packer, Sergei D. Silvestrov and Qiyu Sun).
• Sampling Theory in Signal and Image Processing: Special Issue SampTA 2013, Proceedings of the International Conference on Sampling Theory and its Applications held at Jacobs-University Bremen, Germany, Vol. 13, Nos. 1--4, 2014 (with Götz Pfander and Holger Rauhut).

Journal Articles

• J. Hogan and P. Massopust, Quaternionic B-Splines, submitted 2016.
• P. Massopust, Local Fractal Interpolation on Unbounded Domains, submitted 2015, http://arxiv.org/abs/1508.03198.
• A. Schindele, B. Forster, and P. Massopust, Multigrid Convergence for the MDCA-Curvature Estimator, to appear Journal of Mathematical Imaging and Vision.
• P. Massopust and P. Van Fleet, Fractional Cone and Hex Splines, to appear Rocky Mountain Journal of Mathematics, http://arxiv.org/abs/1504.00546.
• M. Storath, L. Demaret, and P. Massopust, Signal Analysis Based on Complex Wavelet Signs, to appear in Applied and Computational Harmonic Analysis.
• K. Hahn, P. Massopust and S. Prigarin, A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain, BMC Bioinformatics.2016, 17:87.
• P. Massopust, Local Fractal Functions in Besov and Triebel-Lizorkin Spaces, J. Math. Anal. Appl., 436 (2016), 393 - 407.
• P. Massopust and Ahmed I. Zayed, On the Invalidity of Fourier Series Expansions of Fractional Order, Fract. Calc. Appl. Anal., Vol. 18, No 6 (2015), 1507 - 1517.
• P. Massopust, Fractal Hypersurfaces, Wavelet Sets, and Affine Weyl Groups, Lecture Notes for Invited Presentations at the International Conference on Fractals, Wavelets and their Applications, Kerala, India, 2013.
• O. Christensen, B. Forster, and P. Massopust, Directional time frequency analysis via continuous frames, Bull. Aust.Math. Soc., 92 (2015), 268 - 281.
• P. Massopust, On local fractal functions in Banach spaces, AIP Conf. Proc. 1684 (2015), 64002-01 - 64002-04.
• M. F. Barnsley and P. Massopust, Bilinear Fractal Interpolation and Box Dimension, Journal of Approximation Theory, 192 (2015), 363 - 378.
• P. Massopust, Fractional Operators, Dirichlet Averages, and Splines, Applied and Numerical Harmonic Analysis: New Perspectives on Approximation and Sampling Theory (Festschrift in Honor of Paul Butzer's 85th Birthday) (2014), 399 - 422.
• P. Massopust, Exponential Splines of Complex Order, Contemporary Mathematics, Vol. 626 (2014), 87 - 106.
• P. Massopust, Local Fractal Functions and Function Spaces, Springer Proceedings in Mathematics & Statistics: Fractals, Wavelets, and their Applications, Vol. 92(2014), 245 - 270.
• M. F. Barnsley, M. Hegland, P. Massopust, Numerics and Fractals, Bulletin of the Institute of Mathematics, Academica Sinica (N.S.), Vol. 9(3)(2014), 389 - 430.
• M. Storath, L. Demaret and P. Massopust, Wavelet Signs: A New Tool for Signal Analysis, Proceedings of the 10th International Conference on Sampling Theory and Applications, EUROSIP, (2013), 45 - 48.
• B. Forster, R. Garunkstis, P. Massopust, and J. Steuding, Complex B-Splines and Hurwitz Zeta Functions, London Math. Soc. Journal of Computation and Mathematics 16(2013), 61 - 77.
• O. Christensen and P. Massopust, Exponential B-splines and the partition of unity property, Advances in Computational Mathematics 37(3)(2012), 301 - 318.
• P. Massopust, Splines of Complex Order: An Introduction, AIP Conference Proceedings, Vol. 1479 (2012), 991 - 994.
• B. Forster, P. Massopust and T. Übelacker, Periodic splines of complex order, Numerical Functional Analysis and Optimization, 33 (7 - 9)(2012), 989 - 1004.
• P. Massopust, Moments of Complex B-Splines, Commun. Math. Anal., Vol. 12, Number 2 (2012), 58 - 70.
• B. Forster and P. Massopust, Short Communication: Multivariate Interpolation with Fundamental Splines of Fractional Order, Proc. Appl. Math. Mech. Vol. 11 (2011), 857 - 858.
• B. Forster and P. Massopust, Splines of Complex order: Fourier, Filters, and Fractional Derivatives, Sampling Theory in Signal and Image Processing, Vol. 10, No. 1-2 (2011), 89 - 109.
• B. Forster and P. Massopust, Interpolation with fundamental splines of fractional order, Proceedings of SampTA 2011.
• S. Held, M. Storath, P. Massopust, and B. Forster, Steerable wavelet frames based on the Riesz transform,  IEEE Transactions on Image Processing, Volume 19, Issue 3 (2010), 653 - 667.
• D. Larson, P. Massopust, and G. Olafsson, Three-way Tiling Sets in Two Dimensions, Acta Applicandae Mathematicae, 108 (2010), 529 - 546.
• P. Massopust and B. Forster, Multivariate Complex B-splines and Dirichlet Averages, J. Approx. Theory 162 (2010), 252 - 269.
• B. Forster and P. Massopust, Mathematical Aspects of Time Frequency Analysis, in: Four Short Courses in Harmonic Analysis, Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag (2009), 1 - 49.
• B. Forster and P. Massopust, Statistical Encounters with Complex B-Splines, Constr. Approx. 29 (2009), 325 - 344.
• P. Massopust, Double Dirichlet Averages and Complex B-Splines, Proceedings of Sampta 2009.
• B. Forster and P. Massopust, Multivariate Complex B-Splines, Dirichlet Averages and Difference Operators, Proceedings of Sampta 2009.
• B. Forster, P. Massopust, Some Remarks about the Connection between Fractional Divided Differences, Fractional B- Splines, and the Hermite-Genocchi Formula, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 6, No. 2 (2008), 279 - 290
• P. Massopust, P., D. Larson, Coxeter Groups and Wavelet Sets, Contemporary Mathematics, Vol. 451, 187 - 218, 2008
• B. Forster, P. Massopust, Multivariate Complex B-Splines, Proceedings of SPIE, Wavelets XII, Vol. 6701, 670109-1 – 670109-9, 2007
• P. Massopust, Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance, Harmonic Analysis and p-Adic analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 37 - 57, 2007
• P. Massopust, A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions, Advances in Deterministic and Stochastic Analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 131 - 175, 2007

Recent Grants and Sponsored Research

• BayFor (Bayerische Forschungsallianz) Grant for the initiation or immersion of international research collaborations: Efficient representations of multivariate signals, Jan.--Dec. 2015.
• DFG (German Research Foundation) Grant: Splines of Complex Order, Fractional Operators, and Applications in Signal and Image Processing, 2014--2016.
• Start-Up Grant for Cooperation between EuroTech Universities, Technische Universität München, Office of the President, 2012--2014.
• VolkswagenStiftung: Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, 2007.

Recent and Forthcoming Invited Conference and Workshop Presentations

• IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2017.
• Centre International de Rencontres Mathématiques (CIRM), "Multivariate Approximation and Interpolation with Applications," Marseille, France, September 2016.
• 4th Dolomites Workshop on "Constructive Approximation and Applications," Alba di Canazei, Italy, September 2016.
• IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2016.
• AMS Special Session on "Ergodic Theory and Dynamical Systems," AMS Annual Meetings, San Antonio, U.S.A., January 2015.
• International Conference on New Directions in Fractal Geometry, The Australian National University, Canberry, Australia, November 2014.
• International Conference Numerical Analysis and Applied Mathematics 2014, Minisymposium on Fractal Analysis and Harmonic Analysis, Rhodes, Greece, September 2014.
• Fifth International Conference on Computational Harmonic Analysis, Nashville, Tennessee, May 2014.
• International Conference on Fractals and Wavelets, Rajagiri School of Engineering & Technology, Kakkanad Cochin, Kerala, India, November 2013.
• CIMPA 2013, New Trends in Harmonic Analysis, Mar del Plata, Argentina, August 2013.
• AMS Special Session on "Harmonic Analysis of Frames, Wavelets, and Tilings," University of Colorado, Colorado, April 2013.
• Gesellschaft für Angewandte Mathematik und Mechanik (GAMM 2013), Mathematical Image and Signal Processing, Novi Sad, Serbia, March 2013.
• European Intensive Course on Complex Analysis, its Generalizations and Applications, Universidade de Aveiro, Portugal, March 2013 (three two-hour lectures).
• International Conference on Advances on Fractals and Related Topics, Chinese University of Hong Kong, China, December 2012.
• International Conference Numerical Analysis and Applied Mathematics 2012, Kos, Greece, September 2012 (two presentations).
• International Workshop on Operator Theory and Applications, University of New South Wales, Sydney, Australia, July 2012.

Current Collaborations

• University of Newcastle , Newcastle, Australia
• Technical University Denmark (DTU) , Copenhagen, Denmark
• Universität Passau , Passau, Germany
• The Australian National University , Canberra, Australia
• University of St. Thomas , St. Paul, USA
• DePaul University , Chicago, USA
• Vanderbilt University , Nashville, USA

Short and Minicourses, Invited Lecture Series

• Splines and Fractals in Approximation and Interpolation Theory, two-week long GIAN (Global Initiative of Academic Networks) lecture series, IIT Madras, India, July 2016, sponsored by the Government of India.
• Wavelet Sets, Affine Weyl Groups, and Fractal Surfaces (three two-hour invited lectures), $18^{\textrm{th}}$ European Intensive Course on Complex Analysis, its Applications and Generalizations, Universidade de Aveiro, Portugal, March 2013.
• Inverse Problems in Pipeline Inspection (one-hour invited lecture), AMS Short Course The Radon Transform and Applications to Inverse Problems, organized by G. \'{O}lafsson und T. Quinto, sponsored by the American Mathematical Society, Atlanta, Georgia, January 2005.
• Multiwavelets and their Applications (five-day mini-course), invited and sponsored by the Alleghany Section of the Mathematical Association of America, Meadville, Pennsylvania, Juni 1997.
• An Introduction to Fractal Functions and Fractal Surfaces and Their Connection to Wavelet Theory (three-day course), invited and sponsored by the Mathematical Association of America, San Francisco, California, January 1995).

Teaching

Summer Term 2016

• Elements of the Theory of Distributions
• Fourier and Laplace Transforms
• Workshop: Iterated Function Systeme and Fractals

Past Terms

• Elements of the Theory of Distributions (Winter Term 2014/2015)
• Hauptseminar: Models for Evolutionary Dynamics (with Prof. Dr. Ch. Kuttler and Dr. J. Perez-Valezquez) (Summer Term 2014)
• Higher Mathematics 3 for Electrical Engineering (MA9403) (Winter Term 2013/2014)
• Fractal Geometry (Winter Term 2010/2011, Summer Term 2013)
• Complex Function Theory II (Winter Term 2009/2010, Winter Term 2012/2013, Winter Term 2015/2016)
• Lie Groups and Algebras (Summer Term 2012)
• Splines (Summer Term 2011)
• Hauptseminar: Mathematical Methods for Image Processing - Inverse Problems (Summer Term 2011)
• Differential Forms (Winter Term 2007/2008, Summer Term 2010, Winter Term 2011/2012, Summer Term 2015)
• Hauptseminar: Function Spaces (Winter Term 2009/2010)
• Meromorphic Functions and Riemannian Surfaces (Summer Term 2009)
• Proseminar: A Polynomial Approach to Linear Algebra (Winter Term 2008/2009)
• Topology (Summer Term 2008)
• Interpolation and Approximation with Splines and Fractals (Summer Term 2007)
• Proseminar: Complex Function Theory in the Plane and in Space (Summer Term 2007)
• Hauptseminar: Image Analysis (Winter Term 2006/2007)

Curriculum Vitae

• Curriculum Vitae of Peter Massopust